Inclusion Criteria:

• Absolute neutrophil count ≥ 500/mm^3
• Platelet count ≥ 25000/mm^3
• Hemoglobin ≥ 6 g/dL
• Total bilirubin ≤ 2.5 X institutional upper limit of normal (ULN)
• Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) ≤ 5 X ULN
• Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) ≤ 5 X ULN
• Creatinine ≤ 3 mg/dL
• Patients with relapsed or refractory myeloma who have had ≥ 3 lines of prior therapy
• Measurable disease of multiple myeloma as defined by at least ONE of the following:
  • Serum monoclonal protein ≥ 1.0 g/dL
  • > 200 mg of monoclonal protein in the urine on 24 hour electrophoresis
  • Serum immunoglobulin free light chain ≥ 10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio
• Ability to understand and the willingness to sign a written informed consent document
• Negative (serum) pregnancy test done ≤ 7 days prior to registration, for women of childbearing potential only; NOTE: Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
• Willing to return to enrolling institution (Mayo Clinic in Arizona) for follow-up and all study treatments

Exclusion Criteria:

• Myelosuppressive therapy for myeloma ≤ 14 days prior to registration or those who have not recovered from acute reversible adverse events due to agents administered > 21 days earlier
• Other concurrent chemotherapy, radiotherapy, or any ancillary therapy considered investigational; NOTE: Bisphosphonates are allowed while on protocol treatment; patients may be receiving stable doses of corticosteroids with a maximum dose of 10 mg of prednisone per day if they are being given for disorders other than lymphoma such as rheumatoid arthritis, polymyalgia rheumatica or adrenal insufficiency, or asthma
• Other active malignancy ≤ 3 years prior to registration; EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment (i.e. other investigational therapy, anti-neoplastic therapy, etc.) for their cancer
• Any of the following:
  • Pregnant women or women of reproductive ability who are unwilling to use effective contraception
  • Nursing women - NOTE: breastfeeding should be discontinued if the mother is treated with nab-paclitaxel (Abraxane®)
  • Men who are unwilling to use a condom (even if they have undergone a prior vasectomy) while having intercourse with any woman, while taking the drug and for 28 days after stopping treatment
• Other co-morbidity which would interfere with patient's ability to participate in trial, e.g. uncontrolled infection, uncompensated heart or lung disease
• Patients with a ≥ grade 2 peripheral neuropathy